Collinear collisions of an atom and string oscillator

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Abstract
A comparison is made between quantum and classical treatments of impulsive collinear collisions between an atom and string oscillator. The quantum mechanical transition probabilities are evaluated numerically and show a strong dependence upon the masses of the atom and oscillator. This mass dependence is found to parallel the effect observed upon the transition probability when the interaction potential between the atom and the oscillator is varied. A classical argument is used to rationalize this parallel as resulting from the effect of impact multiplicity. The classical transition probabilities and average energy transfer per collision are given explicity for four systems of varying mass. The quantum average energy transfer is generally well approximated by the classical result. However, a large discrepancy appears for certain masses of atom and oscillator.